Question

This is a question for my stats class. Its a hypothesis problem with a conclusion.

Cadmium, a heavy metal, is toxic to animals. Mushrooms, however, are able to absorb and accumulate cadmium at high concentrations. The government has set safety limits for cadmium in dry vegetables at 0.5 ppm. Biologists believe that the mean level of cadmium in mushrooms growing near strip mines is greater than the recommended limit of 0.5 ppm, negatively impacting the animals that live in this ecosystem. A random sample of 51 mushrooms gave a sample mean of 0.59 ppm with a sample standard deviation of 0.29 ppm. What do the biologist should conclude?

Answer 1

Null and alternative hypotheses

Ho : = 0.5

Ha : > 0.5

Test statistic t

t = ( xbar - )/(s/√n)

t = ( 0.59- 0.5)/(0.29/√51)

t = 2.22

tCritical value

For level of significance a = 0.05

Degrees of freedom = n -1 = 51 -1 = 50

tCritical = t​​​​​​0.05 , 50 = 1.68

tCritical = 1.68

Decision rule : If t > 1.68 we reject the null hypothesis otherwise we fail to reject the null hypothesis Ho

Our t = 2.22 > 1.68

Decision : we reject the null hypothesis Ho

Conclusion : There is sufficient evidence to support the claim that the mean level of cadmium in mushrooms growing near strip mines is greater than the recommended limit of 0.5 ppm at 5% level of significance